A new extension of Van Hamme's (E.2) supercongruence

DOI10.1007/s00025-023-02122-yOpenAlexW4392080220MaRDI QIDQ6123329

Chenying Wang

Publication date: 4 March 2024

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-023-02122-y

zbMATH Keywords

supercongruence\(q\)-supercongruencecreative microscoping methodJackson's \({}_6 \phi_5\) summation formula

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)

Cites Work

• Unnamed Item
• Unnamed Item
• On the supercongruence conjectures of van Hamme
• A \(q\)-microscope for supercongruences
• Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
• A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula
• \(q\)-supercongruences on triple and quadruple sums
• A new extension of the (A.2) supercongruence of Van Hamme
• A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
• Dwork-type supercongruences through a creative \(q\)-microscope
• A new \(q\)-extension of the (H.2) congruence of Van Hamme for primes \(p\equiv 1\pmod{4}\)
• \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
• \(q\)-supercongruences from gasper and Rahman's summation formula
• Some congruences that extend Van Hamme's (D.2) supercongruence

This page was built for publication: A new extension of Van Hamme's (E.2) supercongruence